Most image compression algorithms, either lossy or lossless, have focused on the real-valued pixel intensities of the image. As a basis for compression, most of the techniques attempt to exploit local correlations among data elements, e.g., pixel intensities. For example, many lossless compression algorithms for imagery seek to capture the local correlation among pixel intensities using very low order pre-determined linear filters. The error residual output of the filters are then encoded and transmitted to the receiver. Longer prediction filters are not helpful for compressing image pixel intensity data since the correlations are localized.
The transform coding used in JPEG is the most popular approach for lossy image compression. It also tries to capture the local correlations in image intensities by dividing the figure into small 8×8 blocks of data. These localized blocks are transformed using a two-dimensional Discrete Cosine Transform (DCT) and the largest transform coefficients are retained and encoded for transmission. JPEG 2000 is a recent image compression standard based on a wavelet approach that uses sub-banding to decompose the image into low-pass and high-pass regions. The outputs of the filter banks are down-sampled, quantized, and encoded. The decoder decodes the coded representations, up-samples and reconstructs the signal using a synthesis filter bank. In JPEG 2000 the filter banks are predetermined and are independent of the source data. The information necessary to reconstruct the image comes from transmitting selected outputs of the analysis filters. These methods have been useful for compressing electro-optical (EO) imagery; but have not focused on phase preserving compression such as the present invention.